\documentclass[11pt]{amsart}
\usepackage{geometry}
\geometry{letterpaper}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{epstopdf}
\usepackage{fancyhdr}
\usepackage{tikz}
\usepackage{caption}


\def\DrawAirfoil#1{
  % NACA 2412
  \draw plot [smooth, scale=#1] coordinates {
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}


\begin{document}

\begin{description}
  \item[Problem 1] A wing of span $b$ has a distributed lift force
    $l(x)$ along the top and is held down by bridles located at $b/4$
    and $3b/4$.  The bridles may be modeled as point loads going
    straight down with magnitude $T$ N each.  The distributed lift
    force is constant along the span with magnitude $2T/b$ N/m.  What
    are the shear and moment distributions along the wing?

    \begin{figure}[h]
      \begin{tikzpicture}
        % Wing rectangle
        \draw[fill=gray!30] (0.0, 0.0) rectangle (10.0, 0.5)
        node[pos=0.5] {Wing};

        % Distributed lift force.
        \draw (0.0, 1.5) -- (10.0, 1.5) node[midway, above] {$l(x) = 2T/b$};
        \foreach \x in {0.0, 1.0, ..., 10.0} {
          \draw[-latex] (\x, 0.5) -- (\x, 1.5);
        }

        % Bridles point loads.
        \draw[ultra thick, -latex] (2.5, 0.0) -- (2.5, -2.0)
        node[midway, right] {$T$};
        \draw[ultra thick, -latex] (7.5, 0.0) -- (7.5, -2.0)
        node[midway, right] {$T$};

        % Dimensions.
        \draw[latex-latex] (0.0, -0.5) -- (2.5, -0.5)
        node[midway, below] {$b/4$};
        \draw[latex-latex] (2.5, -0.5) -- (7.5, -0.5)
        node[midway, below] {$b/2$};
        \draw[latex-latex] (7.5, -0.5) -- (10.0, -0.5)
        node[midway, below] {$b/4$};
      \end{tikzpicture}
    \end{figure}


  \item[Problem 2] A kite is flying perpendicular to the wind with
    velocity $\vec{v}_{\mathrm{kite}}$.  The wind velocity is
    $\vec{v}_{\mathrm{wind}}$.  A tether, represented by the force
    vector $\vec{T}$, keeps the kite from flying away downwind.  The
    kite has fixed lift and drag coefficients $C_L$ and $C_D$.
    Calculate $\vec{v}_{\mathrm{kite}}$ in terms of
    $\vec{v}_{\mathrm{wind}}$, $C_L$, and $C_D$.

    \begin{figure}[h]
      \begin{tikzpicture}
        \DrawAirfoil {6}
        % Draw velocity vectors.
        \draw[ultra thick, -latex] (-1, 0) -- (-5, 0)
        node[midway, above] {$\vec{v}_{\mathrm{kite}}$};
        \draw[ultra thick, -latex] (-5, -3) -- (-5, 0)
        node[midway, right] {$\vec{v}_{\mathrm{wind}}$};
        \draw[ultra thick, -latex] (-5, -3) -- (-1, 0)
        node[midway, below right] {$\vec{v}_{\mathrm{app}}$};

        % Draw lift, drag, tension vectors.
        \draw[ultra thick, -latex] (6/4, 0) -- ++(4/5, 3/5)
        node[above right] {$\vec{D}$};
        \draw[ultra thick, -latex] (6/4, 0) -- ++(-1, 4/3)
        node[above right] {$\vec{L}$};
        \draw[ultra thick, -latex] (6/4, 0) -- ++(0, -3/5 - 4/3)
        node[midway, right] {$\vec{T}$};
      \end{tikzpicture}
    \end{figure}

\end{description}

\end{document}
